ONE PARAMETER, A WORLD
Hold c still, let z move
For z←z²+c, a Julia set holds c fixed and varies the starting point z. The filled Julia set contains points whose orbits remain bounded; its boundary is the Julia set proper.
GO DEEPER
Connection to Mandelbrot
For the quadratic family, c lies inside the Mandelbrot set exactly when the corresponding filled Julia set is connected. Move c outside and the filled Julia set becomes disconnected.